Chaotic dynamics around astrophysical objects with nonisotropic stresses

The existence of chaotic behavior for the geodesics of the test particles orbiting compact objects is a subject of much current research. Some years ago, Gu\'eron and Letelier [Phys. Rev. E \textbf{66}, 046611 (2002)] reported the existence of chaotic behavior for the geodesics of the test particles orbiting compact objects like black holes induced by specific values of the quadrupolar deformation of the source using as models the Erez--Rosen solution and the Kerr black hole deformed by an internal multipole term. In this work, we are interesting in the study of the dynamic behavior of geodesics around astrophysical objects with intrinsic quadrupolar deformation or nonisotropic stresses, which induces nonvanishing quadrupolar deformation for the nonrotating limit. For our purpose, we use the Tomimatsu-Sato spacetime [Phys. Rev. Lett. \textbf{29} 1344 (1972)] and its arbitrary deformed generalization obtained as the particular vacuum case of the five parametric solution of Manko et al [Phys. Rev. D 62, 044048 (2000)], characterizing the geodesic dynamics throughout the Poincar\'e sections method. In contrast to the results by Gu\'eron and Letelier we find chaotic motion for oblate deformations instead of prolate deformations. It opens the possibility that the particles forming the accretion disk around a large variety of different astrophysical bodies (nonprolate, e.g., neutron stars) could exhibit chaotic dynamics. We also conjecture that the existence of an arbitrary deformation parameter is necessary for the existence of chaotic dynamics.Comment: 7 pages, 5 figure

The double-Kerr equilibrium configurations involving one extreme object

We demonstrate the existence of equilibrium states in the limiting cases of the double-Kerr solution when one of the constituents is an extreme object. In the `extreme-subextreme' case the negative mass of one of the constituents is required for the balance, whereas in the `extreme-superextreme' equilibrium configurations both Kerr particles may have positive masses. We also show that the well-known relation |J|=M^2 between the mass and angular momentum in the extreme single Kerr solution ceases to be a characteristic property of the extreme Kerr particle in a binary system.Comment: 12 pages, 3 figures, submitted to Class. Quantum Gra

Realistic Exact Solution for the Exterior Field of a Rotating Neutron Star

A new six-parametric, axisymmetric and asymptotically flat exact solution of Einstein-Maxwell field equations having reflection symmetry is presented. It has arbitrary physical parameters of mass, angular momentum, mass--quadrupole moment, current octupole moment, electric charge and magnetic dipole, so it can represent the exterior field of a rotating, deformed, magnetized and charged object; some properties of the closed-form analytic solution such as its multipolar structure, electromagnetic fields and singularities are also presented. In the vacuum case, this analytic solution is matched to some numerical interior solutions representing neutron stars, calculated by Berti & Stergioulas (Mon. Not. Roy. Astron. Soc. 350, 1416 (2004)), imposing that the multipole moments be the same. As an independent test of accuracy of the solution to describe exterior fields of neutron stars, we present an extensive comparison of the radii of innermost stable circular orbits (ISCOs) obtained from Berti & Stergioulas numerical solutions, Kerr solution (Phys. Rev. Lett. 11, 237 (1963)), Hartle & Thorne solution (Ap. J. 153, 807, (1968)), an analytic series expansion derived by Shibata & Sasaki (Phys. Rev. D. 58 104011 (1998)) and, our exact solution. We found that radii of ISCOs from our solution fits better than others with realistic numerical interior solutions.Comment: 13 pages, 13 figures, LaTeX documen

Colapso gravitacional radiativo esféricamente simétrico en relatividad general: introducción del factor de flujo, el factor de Eddington y la influencia de la relación de clausura entre ellos sobre la evolución del sistema

The H–J–Rs’ method [Phys. Rev. D22, 2305 (1980)] is extended to include the Eddington’s variable factor, the radiation flux factor and a closure relationship between them in order to show its influence on the behavior of density, pressure, fluid velocity and energy radiation flux, among others, of an object under gravitational collapse within the framework of general relativity. The post-quasistatic approximation of Herrera et al [Phys. Rev. D65, 104004 (2002)] along with the Tolman VI equation of state and the Lorentz–Eddington, Bowers–Wilson and Maximum Packing relationships were used to find that the choice of different closure relationships does not affect the global behavior of the system but only the instantaneous values of the different physical quantities.  Se extiende el método H–J–R [Phys. Rev. D22, 2305 (1980)] utilizando el factor variable de Eddington y el factor de flujo de radiación, y se presenta la influencia de la elección de la relación entre ellos sobre el comportamiento en el tiempo de la densidad, presión, velocidad del fluido y flujo de radiación, entre otras, de un objeto en fase de colapso gravitacional radiativo en el marco de la relatividad general. Para tal fin, se ha utilizado la aproximación poscuasiestática de Herrera et al [Phys. Rev. D65, 104004 (2002)] con la ecuación de estado Tolman VI y las relaciones de clausura de Lorentz–Eddington, Bowers–Wilson y Maximum Packing, encontrando que la elección de una relación de clausura particular no afecta el comportamiento General del colapso, pero sí afecta los valores instantáneos de las diferentes magnitudes físicas.         &nbsp

A system dynamics-based scenario analysis of residential solid waste management in Kisumu, Kenya

The problem of solid waste management presents an issue of increasing importance in many low-income settings, including the progressively urbanised context of Kenya. Kisumu County is one such setting with an estimated 500 t of waste generated per day and with less than half of it regularly collected. The open burning and natural decay of solid waste is an important source of greenhouse gas (GHG) emissions and atmospheric pollutants with adverse health consequences. In this paper, we use system dynamics modelling to investigate the expected impact on GHG and PM_{2.5} emissions of (i) a waste-to-biogas initiative and (ii) a regulatory ban on the open burning of waste in landfill. We use life tables to estimate the impact on mortality of the reduction in PM_{2.5} exposure. Our results indicate that combining these two interventions can generate over 1.1 million tonnes of cumulative savings in GHG emissions by 2035, of which the largest contribution (42%) results from the biogas produced replacing unclean fuels in household cooking. Combining the two interventions is expected to reduce PM_{2.5} emissions from the waste and residential sectors by over 30% compared to our baseline scenario by 2035, resulting in at least around 1150 cumulative life years saved over 2021–2035. The contribution and novelty of this study lies in the quantification of a potential waste-to-biogas scenario and its environmental and health impact in Kisumu for the first time